Earlier quoted context omitted.
You are right in practice. But it sounds an awful lot bit like the old "I have nothing to hide" argument against encryption, too? Many payment processors do restrict the business they want to deal with beyond what the letter of the law requires. (And that is their prerogative as a private business!)
If they refuse business to let's say gays the government would come after them. How is refusing to serve legal sex workers different?
> How is refusing to serve legal sex workers different?
As far as I can tell, in the US discrimination is forbidden against certain protected groups / along certain protected differences only. But you are free to discriminate on all other grounds. Eg a restaurant can legally discriminate against people who don't wear a tie.
The UK rules are similar, see eg https://www.gov.uk/discrimination-your-rights
In the British rules, sexual orientation is explicitly mentioned, but your trade ain't. So as far as I can tell, it's illegal in the UK to discriminate against gays but legal to discriminate against sex workers.
(However, a government might come after you, if you do something they don't like, even if it's perfectly legal. Eg the government could just 'randomly' decide to audit your taxes all the time, or 'randomly' apply other regulations and rules more strictly.)
See https://en.wikipedia.org/wiki/Protected_group for a list of the protected groups in the US. Wikipedia lists sexual orientation, but not vocation.